bearing capacity of thin-walled shallow foundations: an

Rezaei et al. / J Zhejiang Univ-Sci A (Appl Phys & Eng) 2016 17(4):273-285 273

Bearing capacity of thin-walled shallow foundations:

an experimental and artificial intelligence-based study*

Hossein REZAEI1, Ramli NAZIR2, Ehsan MOMENI†‡1,2 (1Faculty of Engineering, Lorestan University, Khorram Abad 68151-44316, Iran)

(2Department of Geotechnics and Transportation, Faculty of Civil Engineering, Universiti Teknologi Malaysia, Johor 81310, Malaysia) †E-mail: [email protected]

Received Feb. 10, 2015; Revision accepted July 10, 2015; Crosschecked Mar. 16, 2016

Abstract: Thin-walled spread foundations are used in coastal projects where the soil strength is relatively low. Developing a predictive model of bearing capacity for this kind of foundation is of interest due to the fact that the famous bearing capacity equations are proposed for conventional footings. Many studies underlined the applicability of artificial neural networks (ANNs) in predicting the bearing capacity of foundations. However, the majority of these models are built using conventional ANNs, which suffer from slow rate of learning as well as getting trapped in local minima. Moreover, they are mainly developed for conventional footings. The prime objective of this study is to propose an improved ANN-based predictive model of bearing capacity for thin-walled shallow foundations. In this regard, a relatively large dataset comprising 145 recorded cases of related footing load tests was compiled from the literature. The dataset includes bearing capacity (Qu), friction angle, unit weight of sand, footing width, and thin-wall length to footing width ratio (Lw/B). Apart from Qu, other parameters were set as model inputs. To enhance the diversity of the data, four more related laboratory footing load tests were conducted on the Johor Bahru sand, and results were added to the dataset. Experimental findings suggest an almost 0.5 times increase in the bearing capacity in loose and dense sands when Lw/B is increased from 0.5 to 1.12. Overall, findings show the feasibility of the ANN-based predictive model improved with particle swarm optimization (PSO). The correlation coefficient was 0.98 for testing data, suggesting that the model serves as a reliable tool in predicting the bearing capacity.

Key words: Thin-walled foundation, Sand, Bearing capacity, Artificial neural network (ANN), Particle swarm optimization

(PSO) http://dx.doi.org/10.1631/jzus.A1500033 CLC number: TU43

1 Introduction

Foundations are generally categorized into deep and shallow (spread) foundations. The use of the latter is recommended from the economic perspec-tive if the subsurface condition is good enough (Gib-bens and Briaud, 1995). Nevertheless, bearing ca-pacity and allowable settlement of foundations are of

great concern to geotechnical engineers (Momeni et al., 2013). The former is often referred to a maxi-mum load that the soil can tolerate before its failure. A number of researchers (Terzaghi, 1943; Meyerhof, 1963; Vesic, 1973) formulated bearing capacity the-ory, which for reasons of brevity is not repeated here as it is well established.

However, in the recent past, the use of skirted shallow foundations, or in other words thin-walled spread foundations, is highlighted in several studies. In this regard, Al-Aghbari and Mohamedzein (2004) as well as Eid et al. (2009) mentioned that providing skirts (thin-walls) for the spread foundation forms an enclosure in which the soil is confined. They hypothesized that the existence of such walls results

‡ Corresponding author * Project supported by the Science Fund of Malaysian Ministry of Science, Technology and Innovation (No. #4S077)

ORCID: Hossein REZAEI, http://orcid.org/0000-0003-0766-5833; Ehsan MOMENI, http://orcid.org/0000-0003-4084-485X

© Zhejiang University and Springer-Verlag Berlin Heidelberg 2016

Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)

ISSN 1673-565X (Print); ISSN 1862-1775 (Online)

www.zju.edu.cn/jzus; www.springerlink.com

E-mail: [email protected]


in transferring the foundation loads to the laterally confined soil and then to the deeper sand layers that are more confined than shallow layers due to an increase in overburden pressure. Providing thin-walls for foundations can increase the total depth of failure and change the failure pattern of the soil which may lead to more shear strength mobilization.

Al-Aghbari and Mohamedzein (2004) reported the increase in bearing capacity by a factor in the range of 1.5 to 3.9 when skirt foundations are used instead of simple (surface) foundations. In another study, Al-Aghbari and Dutta (2008) addressed an increase in the bearing capacity from 11.2% to 70% due to incorporation of structural skirts.

Eid (2013) mentioned that incorporation of skirts leads to significantly higher bearing capacity. According to his conclusion, depending on thin-wall length to footing width ratio (Lw/B), thin-walled foundations exhibited 1.4 to 3 times higher bearing capacity in comparison with simple foundations.

Nazir et al. (2013) introduced a specific thin-walled spread foundation (Fig. 1) suitable for indus-trialized building systems. Their numerical investi-gations showed the workability of the aforemen-tioned foundation. Momeni et al. (2015b) reported that the use of a thin-walled spread foundation com-pared with a surface foundation can increase the bearing capacity by almost twice in both loose and dense sands.

Nevertheless, the fact that famous bearing ca-pacity equations are proposed for conventional spread foundations rather than thin-walled spread foundations encouraged the authors to develop a predictive model of bearing capacity for such foot-ings. As highlighted in the next section, the use of an artificial neural network (ANN) in foundation engi-neering problems, i.e., bearing capacity, is recom-mended in many studies (Shahin, 2015).

However, the majority of the predictive models of bearing capacity are built using a conventional ANN which suffers from getting trapped in local minima and a slow rate of learning. In this regard, several studies reported the use of optimization algo-rithms, such as the genetic algorithm (GA) and parti-cle swarm optimization (PSO) algorithm, for en-hancing the ANN performance (Section 3.4).

In this study, an attempt was made to develop an improved ANN-based predictive model of bear-ing capacity for thin-walled spread foundations. For this reason, four small scale footing load tests were conducted in the laboratory. The laboratory tests results as well as a relatively large number of related recorded cases of footing load tests compiled from literature formed the required dataset for developing the predictive model proposed in this study.

It is worth mentioning that as far as authors are aware, there is no comprehensive and well-established ANN-based predictive model for this kind of foundation (thin-walled spread foundations). Thus, the study presented here is different from pre-viously proposed predictive models of bearing ca-pacity. In addition, the work presented here takes advantage of a relatively large dataset, i.e., 149 rec-orded cases, which significantly reduces the likeli-hood of model over fitting (Zorlu et al., 2008).

2 Related predictive models Successful application of a conventional ANN

in geotechnical engineering is addressed in many studies (Shahin et al., 2001; Jahed Armaghani et al., 2014; Tonnizam Mohamad et al., 2014). As tabulat-ed in Table 1, in foundation engineering, numerous researchers showed the workability of ANNs for predicting either settlement or bearing capacity of foundations. Table 1 also gives the dataset number, the coefficient of determination values, as well as

Fig. 1 Thin-walled spread foundation: (a) isometric view;(b) bracing system; (c) bottom view; (d) cross sectional view. Reprinted from (Momeni et al., 2015b), Copyright 2015, with permission from ICE Publishing


the major input parameters of the recently proposed predictive models. According to Table 1, footing geometrical and soil properties are influential pa-rameters in ANN-based predictive models.

3 Methods

3.1 Artificial neural network

The application of ANN as a promising tool in solving geotechnical and rock engineering problems has drawn considerable attention (Meulenkamp and Alvarez Grima, 1999). In essence, the use of ANNs as function approximation tools is of interest when the contact nature between the influential parameters on model output(s) and the output parameter(s) is unknown. In other words, when the underlying problem is difficult to model explicitly or it is diffi-cult to find a close form solution for a problem, the use of ANNs is advantageous (Garrett, 1994). Nev-ertheless, a typical ANN consists of a number of interconnected layers (input, hidden(s), and output(s) layers). Each layer comprises one or more pro-cessing units known as neurons or nodes. The nodes of different layers are connected to each other through adjustable connection weights. However, as reported by Hornik et al. (1989), usually one hidden layer is good enough for approximating any continu-ous function.

The use of more hidden layers can increase the model complexity and the likelihood of model over fitting, which should be avoided in designing ANNs.

Before interpreting new information, the network needs to be trained.

The back-propagation (BP) algorithm is the most commonly implemented training algorithm in ANNs (Dreyfus, 2005). In essence, the role of the BP algorithm is to optimize the connection weights which lead to a desirable mean square error (MSE). The MSE is referred as the square difference be-tween the predicted outputs and the target outputs. The best outputs are often predicted after several feedforward-backward passes. In the forward pass, the data presented to input layer (denoted by Ii in Fig. 2, i=1, 2, …) start to feedforward. In this step, each input node transmits several signals to the hid-den nodes. In other words, each node in the hidden layer (Ni in Fig. 2) receives the sum of weighted in-put signals (input values multiplied by random con-nection weights, ∑Wij in Fig. 2) as well as a thresh-old value known as bias (Bi in Fig. 2). The output of each hidden neuron is subsequently obtained by ap-plying a transfer function (usually a sigmoid func-tion) on the net input values of hidden neurons (Fig. 2). The same procedure is repeated for the next layers until the output (O in Fig. 2) is predicted. Having known the actual outputs, if the predicated outputs are not desirable, the network should back propagate and update the connection weights. This process is known as backward pass. These passes are repeated until the desirable outputs are predicted. Readers are referred to fundamental artificial intelli-gence books for more information about ANNs (Fausett, 1994).

Table 1 Related works on the application of ANN in foundation engineering

Source Dataset number Major inputs Footing type Reliability, R2

Goh (1996) 116 PS, HW Pile 0.93

Lok and Che (2004) 105 G, SW Pile 0.92

Soleimanbeigi and Hataf (2006) 351 G, , Spread 0.94

Padmini et al. (2008) 97 , G, Spread 0.98

Ornek et al. (2012) 28 G, S Spread 0.95

Kiefa (1998) 59 G, , ′ Pile 0.91

Pal and Deswal (2008) 105 G, SW Pile 0.98

Zhao et al. (2010) 9 N, , G, , C Pile –

Benali and Nechnech (2011) 80 G, C, ′ Pile 0.84

Momeni et al. (2014) 50 G, HW, PS, HD Pile 0.99

Momeni et al. (2015a) 36 G, PS, N Pile 0.94

N: standard penetration test N value; G: geometrical properties of footings (piles or shallow foundations); q: footing net applied pressure; : soil friction angle; : unit weight of soil; ′: effective stress of the soil; S: settlement of the footing; SW: stress-wave data; C: soil co-hesion; HW: hammer weight; HD: drop height; PS: pile set


3.2 Particle swarm optimization

Particle swarm optimization (PSO) is an evolu-tionary computation algorithm which implements a nonlinear procedure for solving a continuous global optimization problem. PSO was proposed by Kenne-dy and Eberhart (1995). In PSO, particles are candi-date solutions of a problem. At first, a random num-ber of particles forms a population. Each particle is given a random position and velocity. Subsequently, an iterative procedure is implemented to find the best solution (often global minima). The particle posi-tions, at this stage, are adjusted based on the particle experience as well as the swarm experience. To be more specific, each particle keeps track of its best position as well as the global best position of other particles. In PSO terminology, the best position which a particle has experienced and the global best experience achieved by other particles are referred as pbest and gbest, respectively.

Nevertheless, PSO is trained to propel towards its pbest and gbest. For this reason, a new velocity term is determined for each particle based on its distance from its pbest and gbest. In the next step, these two pbest and gbest velocities are randomly weighted to gener-ate a new velocity value for a specific particle. As a consequence, in the next iteration, the position of the particle will be affected (Eberhart and Shi, 2001). The relatively simple PSO velocity update and movement equations are given in the following lines. They are mainly used for determining the actual

movement of a particle and adjusting the velocity vector.

Vnew=V+r1c1×(pbest–p)+r2c2×(gbest–p), (1) pnew=p+Vnew, (2)

where c1 and c2 are pre-defined coefficients, r1 and r2 are random values in the range (0, 1) sampled from a uniform distribution, Vnew and V are the new and current velocity vectors, pnew and p are the new and current positions of particles, respectively.

3.3 Genetic algorithm

The genetic algorithm (GA), which was first in-troduced by Holland (1975), is one of the most popu-lar evolutionary algorithms. Similar to PSO, in GA there are some candidate solutions that mature over time to reach an optimal solution. In GA terminolo-gy, the candidate solutions, which form an initial population, are called chromosomes. Chromosomes are in the form of a linear string comprising 0 and 1. Similar to other optimization algorithms, GA starts with defining the optimization parameters and cost function (usually MSE), and ends when the stopping criteria are met. Each iteration in GA is termed gen-eration. However, to produce the next generation in GAs, three genetic operations should be performed. These operators include reproduction, crossover, and mutation.

As stated by Momeni et al. (2014), reproduc-tion is a step in which the best chromosomes are se-lected according to their scaled values and based on the given criteria of fitness, subsequently they will be passed to the next generation. Crossover, on the other hand, generates offspring (also called new in-dividuals) by combining certain parts of the parents. In essence, as mentioned by Jadav and Panchal (2012), in the crossover process, two parents as well as an arbitrary crossover point are selected. Subse-quently, through merging the left side genes of the first parent with right side genes of the second parent, the first offspring is generated. For creating the sec-ond offspring, an inverse procedure is repeated. The last GA operator is mutation. This operator is uti-lized to describe a sudden change which might ap-pear in the allele of a chromosome. The negligible arbitrary changes applied to the element of a chro-mosome help GA to search a broader space. A typi-cal GA is described in the following lines:

Fig. 2 Typical architecture of ANN. Reprinted from(Momeni et al., 2014), Copyright 2014, with permissionfrom Elsevier


1. Forming a group of candidate solutions (ini-tial population);

2. Finding the cost of each chromosome: (1) Preferentially transferring the chromosomes

with lower costs to the next generation; (2) Applying crossover and mutation function

for creating new chromosomes; 3. Checking convergency (if the stopping crite-

rion is not met, repeat the second step); 4. Introducing the fittest chromosome as the

solution.

3.4 Hybrid artificial neural network

It was mentioned above that the main reasons behind using the optimization algorithms are the ANN deficiencies in getting trapped in local minima as well as the ANN slow rate of learning (Lee et al., 1991). However, recent literature suggested several optimization algorithms (i.e., PSO, GA) for enhanc-ing ANN performance like the study of Rashidian and Hassanlourad (2013) on a GA enhancing ANN performance and improving on its drawbacks. Such a conclusion was also highlighted in other recent stud-ies (Majdi and Beiki, 2010; Jadav and Panchal, 2012; Liu et al., 2012). PSO beneficial effects were cov-ered by Momeni et al. (2015c). PSO as a global search algorithm can be implemented to improve ANNs’ performance by adjusting the weight and bias of ANNs (Shi and Eberhart, 1999; Mendes et al., 2002). In fact, PSO and GA as global search algo-rithms help ANN as a local search algorithm to avoid it getting trapped in local minima and to find global minima.

It was discussed earlier that finding the mini-mum MSE is the main aim in ANNs. In the im-proved ANNs, the ANN connection weights are trained with the optimization algorithms rather than with a conventional back-propagation learning algo-rithm. The reason is to increase the chance of finding global minima (the least MSE).

4 Model dataset

To obtain a sufficient size of dataset for devel-oping the predictive model of bearing capacity, an extensive literature review gave a database compris-

ing 145 recorded cases of thin-walled footing load tests (Villalobos, 2007; Al-Aghbari and Moham-edzein, 2004; Eid et al., 2009; Tripathy, 2013; Wakil, 2013; Momeni et al., 2015b). The results of four laboratory tests (to be discussed later) were also add-ed to the dataset to enhance the diversity of the data. Table 2 summarizes the minimum, maximum, as well as the average values of the dataset used in this study. Needless to say, the bearing capacity of thin-walled spread foundations in cohesionless soils is related to footing width B, soil internal friction angle , soil unit weight , and Lw/B. Therefore, these pa-rameters were used as the input parameters of the predictive models. The bearing capacity (Qu) of the thin-walled spread foundations in cohesionless soils was set as the model output.

5 Model development procedure

In the first step, a parametric study was utilized for determining the suitable PSO-based ANN pa-rameters comprising swarm size, network architec-ture, and the number of iterations. For this purpose, a MATLAB code was prepared. Subsequently, based on an educated guess, an ANN model with one hid-den layer and seven hidden neurons was set to be an initial model. Random sampling was used for divid-ing the dataset into two subsets: training and testing. The use of this procedure was suggested in several studies (Alvarez Grima and Babuška, 1999; Singh et al., 2001; Rabbani et al., 2012; Tonnizam Mohamad et al., 2014). Nevertheless, it should be mentioned that 80% of the data were used for network training and the other 20% were used for testing the prediction power of the model. The first step in the parametric study was to determine the number of iterations as well as the optimum swarm size. The former is often used as the termination criterion. The termination

Table 2 Summarized dataset

Value B

(mm)Lw/B ()

(kN/m3)

Qu (kPa)

Min 36.55 0 29.23 10.34 17.1

Max 144 2 44.75 18.2 8005

Average 71.16 0.9 38 15.5 607


criterion is a condition that, upon being met, ends the iterative procedure. Therefore, an effort was made to investigate the effect of iteration numbers on the network performance.

A model with a default 800 iterations, 150 particle size, and acceleration constants (c1 and c2) equal to 2 was built. Fig. 3 suggests there is no remarkable change in the MSE after 450 iterations. Hence, 450 iterations was set to be the maximum number of iterations.

The best swarm size also needs to be deter-

mined. It is worth mentioning that enlarging the swarm size (number of particles) increases the model complexity as well as the training time, while small swarm size may negatively affect the performance of the model. Hence, a sensitivity analysis was per-formed to find the optimum number of particles. For this purpose, the effect of a wide range of swarm sizes (70–800 from small to large) on model perfor-mances was studied, and the MSE was determined in each analysis.

Other PSO parameters were not changed during this step. That is, to find the best PSO structure, the number of iterations was set to be 450 and accelera-tion constants (c1 and c2) equal to 2 were used as suggested by Shi and Eberhart (1998) and Mendes et al. (2002). Fig. 4 shows the values of MSE obtained for different swarm sizes.

As displayed in Fig. 4, the model built with 600 particles performed best with an MSE of 0.009. Therefore, the number of particles was set to be 600. It should be mentioned that before modelling, the data were normalized to values between −1 and 1.

After determining the optimum PSO parameters,

the network architecture was designed. To obtain the proper network design, four hybrid models were run with different numbers of hidden neurons in one lay-er. However, for evaluating the performance of the model, R values of the testing dataset were studied.

Nevertheless, 4, 5, 6, or 7 neurons were trialed in each hidden layer to obtain the proper number of neurons. Table 3 shows the analyses results. The tabulated results in Table 3 indicate that the model which was built with seven neurons in the hidden layer (the fourth model) outperforms the other mod-els. The correlation coefficient and MSE, equal to 0.98 and 0.005, respectively, for the testing dataset suggest the model superiority. Therefore, the archi-tecture of this model was considered to be optimum for the predictive model of bearing capacity.

In developing a GA-based ANN predictive

model, a procedure similar to the PSO-based ANN was utilized to determine the GA parameters. How-ever, in the interests of brevity, it is not repeated here. Nevertheless, after conducting the parametric study, it was found that the best GA-based ANN for the problem of interest is expected when the GA param-eters presented in Table 4 are used. After finding the

Table 3 Prediction performance of different PSO-based ANN models

ModelNumber of nodes

Training Testing

MSE R MSE R

1 4 0.016 0.88 0.020 0.81

2 5 0.008 0.92 0.037 0.86

3 6 0.013 0.88 0.020 0.97

4 7 0.015 0.91 0.005 0.98

Fig. 3 Effect of iteration numbers on model performance

0

0.005

0.010

0.015

0.020

0.025

0 100 200 300 400 500 600 700 800 900

Swarm size

Fig. 4 Effect of swarm size on model performance


suitable GA parameters, similar to the ANN model improved with PSO, the optimum number of hidden neurons in the GA-based ANN model was obtained. This is tabulated in Table 5 where the performances of various models were evaluated using the MSE values and correlation coefficients. As displayed in Table 5, the models consisted of various hidden nodes, i.e., 4, 5, 6, and 7 in one hidden layer. Ac-cording to Table 5, the last model, i.e., Model 4, works better. The correlation coefficient and MSE of 0.87 and 0.010, respectively, for testing dataset indi-cate that the aforementioned model performs best. The results of this predictive model will be discussed in Section 7.

To have a better understanding, the prediction

performances of the hybrid models were compared with those of a conventional ANN. For this purpose, using an ANN model constructed with seven hidden neurons in one hidden layer, the bearing capacity of the thin-walled spread foundations were predicted. The Levenberg-Marquardt (LM) learning algorithm was used for training the network. More details on this learning algorithm (its efficiency for training) were discussed in the study conducted by Hagan et al. (1996). Nevertheless, like improved ANN models, in the conventional ANN model, random sampling was used (80% of the data for training the model and the rest for testing purpose).

6 Laboratory test procedure In this section the procedure implemented in

conducting the footing load tests is highlighted. In this study, the load carrying capacity of a specific thin-walled foundation proposed by Nazir et al. (2013) (Fig. 1) is investigated. The footing is re-ferred to as an industrialized building systems (IBS) footing mainly because it is developed to be used in IBS. In essence, two IBS footings as shown in Fig. 5 were loaded in the Johor Bahru sand (in loose and dense states). The sand particles ranged from 0.063 mm to 1.18 mm. The mean grain size (D50), effective grain size (D10), and coefficient of uni-formity Cu were 0.5 mm, 0.142 mm, and 3.52, re-spectively. The unit weight and internal friction an-gle for loose and dense sands were 14.26 kPa and 29.23, 15.54 kPa and 36.24, respectively. Several studies addressed the minimization of scale effect if the ratio of footing width to soil mean grain size ex-ceeds 100 (Habib, 1974; Taylor, 1995; Kalinli et al., 2011). Therefore, knowing the D50 of the sand, small scale IBS footings of width 80 mm (18.75 times smaller compared with proposed full scale in Fig. 1) were prepared. Fig. 5 also shows the dimensions of the footings used in this study. As shown in Fig. 5, apart from Lw/B, other dimensions are the same for both footings.

The footings were given a rough surface by glu-

ing sand to their base and sides. All tests were

Table 4 Optimum GA parameters

Parameter Description

Mutation probability 1%

Recombination percentage 9%

Single point crossover 90%

Selection method Tournament

Population size 230

Generation number 45

Table 5 Prediction performance of various GA-based ANN models

Model Number of nodes

Training Testing

MSE R MSE R

1 4 0.043 0.65 0.023 0.70

2 5 0.050 0.60 0.018 0.82

3 6 0.038 0.69 0.025 0.76

4 7 0.040 0.71 0.010 0.87

Fig. 5 Thin-walled shallow foundations used in this study(a) IBS footing with shorter wall; (b) IBS footing with longer wall

(a) (b)


performed in a test box with length, width, and height of 920, 620, and 620 mm, respectively (Fig. 6). The box was large enough to minimize the boundary condition effects and it was made of Plexi-glas to provide better view of soil deformation. To reconstruct the sand at desired relative densities, i.e., 30% (loose) and 75% (dense), a new mobile sand pluviator system (Fig. 6), invented by Khari et al. (2014), was used. The use of this technique for achieving the desired relative density has been high-lighted by many researchers (Madabhushi et al., 2006). The footings were placed at the center of the box and were driven (pushed) on the sand. Eid et al. (2009) mentioned that using this procedure will not lead to more than 4% bearing capacity overestima-tion. The testing tank was then placed over a frame made of 6-inch U-type steel profile (1 inch=2.54 cm).

The load was applied slowly to the model foot-

ings by means of a pneumatic loading shaft in a con-tinuous operation. The load was measured with a 20-kN load cell with an accuracy of ±0.01% resting between the footing and the load frame. The footing settlement was measured based on the readings of two linear variable displacement transducers (LVDT) installed on a reference beam (Fig. 7). The LVDT’s accuracy was ±0.01% of full range (100 mm).

The load was increased if the rate of settlement change was less than 0.003 mm/min over 3 consecu-

tive minutes. The use of this procedure was reported in several studies (Adams and Collin, 1997; Briaud and Gibbens, 1999; Chen et al., 2007). However, footings were loaded in relatively loose and dense sands until the soil settlement reached almost 25 mm.

7 Results and discussion The superimposed load-displacement curves of

footing load tests in loose sand are shown in Fig. 8. Overall, the results are not surprising. That is to say, for longer wall length, higher bearing capacity is expected. Fig. 8 suggests that the load carrying ca-pacity of an IBS footing with shorter walls is 560 N while as expected, for an IBS footing with longer walls, the bearing capacity was found to be almost 830 N.

Fig. 6 Mobile sand pluviator and test tank

Fig. 7 Laboratory footing load test

0

-5

-10

-15

-20

-25

-30

Load (N)

0 200 400 600 800 1000 1200

IBS footing (longer walls)

Set

tlem

ent

(mm

)

IBS footing (shorter walls)

Fig. 8 Load-displacement curve of thin-walled footings inloose sand


It is interesting to note that results suggest that selecting a value beyond 10% of footing width leads to bearing capacity overestimation. In fact, Fig. 8 suggests that the soil failure is captured when the soil deformation reached almost 8%B. Although the figure is self explanatory, it should be highlighted that for interpreting the failure load, the recently proposed L1-L2 method (Akbas and Kulhawy, 2009) was utilized. In this method, the initial point (L2) of the last part of load-displacement curves is referred to as the axial bearing capacity of the footing. As displayed in Fig. 8, the effect of thin-walls on the transition part of load-displacement curves is obvi-ous. Although the initial parts of curves are different to some extent that may generally be attributed to some uncertainties in conducting the tests. For ex-ample, reconstructing the sand in exactly the same density using sand raining technique is almost im-possible and it is always expected to have sand a bit denser or looser than what is intended. This effect is more pronounced in loose sand compared with dense sand as the rate of sand raining, when constructing the loose sand, is much more than that of dense sand. Therefore, it is more difficult to achieve exactly the same relative density when the loose sand has to be reconstructed several times.

Nevertheless, similarly, the load-displacement curves of thin-walled footings in dense sands are presented in Fig. 9. According to Fig. 9, the bearing capacity of an IBS footing with shorter walls (Lw/B=0.5) is 1990 N. For an IBS footing with long-er walls (Lw/B=1.12), the load carrying capacity was found to be 2985 N.

Overall, Fig. 9 suggests that the general shear failure of sand is what is expected and it may be at-tributed to the dense state of the soil. Additionally, no specific bulging was observed for the IBS footing with either higher or shorter wall length (Fig. 10 as an example), which might be due to the incorpora-tion of thin-walls. However, as stated in the study of Wakil (2013), it should be highlighted here that the bearing capacity failure is not necessarily grouped in three specific categories as proposed by Vesic (1973), i.e., general, local, and punching shear failure, main-ly because these categories are suggested for un-skirted footings.

Nevertheless, in thin-walled foundations, the

soil located between walls is confined; hence, the footing and the confined soil inside the walls are acting as one integrated system. Consequently, as the length of walls increases, in a sense, the foundation embedded depth increases. Therefore, the bearing capacity of thin-walled foundations is enhanced as the wall length increases. However, in terms of neg-ligible uncertainties in conducting the IBS footing load tests, a conclusion similar to loose sand can be drawn for dense sand as well, which in the interests of brevity is not repeated here. Overall, it was found that when Lw/B of the footings in both loose and dense sands is increased from 0.5 to 1.12, the bear-ing capacity is increased almost 0.5 times.

This is in reasonable agreement with Wakil (2013)’s findings where he reported an almost 0.3 times increase in bearing capacity of thin-walled foundations in dense sands when Lw/B is increased from 0.5 to 1.

Fig. 10 IBS footing in dense sand after soil failure

Fig. 9 Load-displacement curve of thin-walled footingsin dense sand

0

-5

-10

-15

-20

-25

-30

Load (N)

0 500 1000 1500 2000 2500 3000 3500

Set

tlem

ent

(mm

)

IBS footing (longer walls)

IBS footing (shorter walls)


The results of different predictive models of bearing capacity described in the previous sections are also highlighted in this section. Fig. 11 shows the normalized predicted Qu using PSO-based ANN, GA-based ANN as well as conventional ANN mod-els versus the normalized measured bearing capaci-ties of thin-walled spread foundations for the train-ing dataset.

The correlation coefficient of PSO-based ANN model (R=0.91) suggests that the proposed PSO-based ANN model works better in predicting Qu compared with GA-based ANN and conventional ANN. The R values of GA-based ANN and conven-tional ANN are only 0.71 and 0.84, respectively.

The prediction performance of the proposed models for the testing dataset is shown in Fig. 12. The correlation coefficient R is equal to 0.98 in Fig. 12a, which also suggests the good reliability and

relative superiority of the proposed PSO-based ANN model in predicting Qu. The correlation coefficients for GA-based ANN and conventional ANN of test-ing data are only 0.87 and 0.64, respectively. This is in good agreement with Nazir et al. (2014) as well as Marto et al. (2014) who suggested the feasibility of the PSO-based ANN model in foundation engineer-ing problems. Overall, the PSO-based ANN model performs best. Therefore, this study suggests the use of the PSO-based ANN model in predicting the bear-ing capacity of thin-walled foundations.

8 Conclusions

The close agreement between the measured and predicted (using the PSO-based ANN model) bear-ing capacities revealed the applicability of hybrid

R=0.84

(a)

Fit

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Fig. 11 Prediction performance of PSO-based ANN (a), GA-based ANN (b), and conventional ANN models (c) (trainingdataset)

Fig. 12 Prediction performance of PSO-based ANN (a), GA-based ANN (b), and conventional ANN models (c) (testingdataset)

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中文概要

题目：基于人工智能的薄壁浅地基的承重能力研究

目的：薄壁扩展式地基已被广泛应用于土壤强度相对

较低的沿海工程。目前，已有很多学者对其进

行了人工神经网络的适用性研究，希望用此对

地基的承重能力进行预测。但是这些研究多数

是基于传统的人工神经网络，学习速度慢且受

困于局部极小值。本文拟提出一种改进的基于

人工神经网络的预测薄壁浅地基承重能力的

模型。

方法：1. 整合 145 组关于地基承重测试的文献数据和

实验数据（包括承重能力、摩擦角、沙的单位

重量、基脚宽度和长宽比等）；除了承重能力，

其他参数都是模型输入；2. 研究各参数对地基

承重能力的影响，确定最优的人工神经网络模

型参数，并对不同的人工神经网络模型进行

比较。

结论：1. 当基脚长宽比从 0.5 变为 1.12 时，地基的承重

能力增加了大约一半；2. 基于粒子群优化算法

的人工神经网络模型表现最好；在测试数据

中，承重能力的预测值和测量值之间高达 0.98

的相关系数也表明，在无粘性土中，基于人工

神经网络的预测模型适用于薄壁浅地基的承重

能力预测。

关键词：薄壁地基；沙；承重能力；人工神经网络；粒

子群优化

bearing capacity of thin-walled shallow foundations: an

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